The Earth's Orbit

We are at a point in the earth's orbit that is closest to the sun.
The autumn and spring equinoxes are separated by approximately 1/2 year. In fact, there are three more days in the period from the spring equinox, about March 20,21, to the fall equinox, about September 20,21, than there are in the September to March time. This discrepancy was probably known to the ancients, as all calendars marked these times as important for migrations, agriculture and other cultural needs. The actual explanation for the differing day count came from Johannes Kepler, 1571-1630. Kepler realized that the orbit of the earth was not a perfect circle but an ellipse with the sun at one focal point. This meant that we were closer to the sun at certain times of the year and orbiting faster during those periods. He did not fully realize that gravity was the cause of our orbital motion so only could hypothesize rules based on observations that would describe the orbital motions of the planets. The physics community would have to wait for Isaac Newton, 1642-1727, for the idea of "action at a distance" and a quantifying rule for gravity.
In a modern introductory Celestial Mechanics course, Kepler's three laws form the basis for that course. The laws are:

1. The orbits of the planets are ellipses with the sun at one focus.
2. The equal area rule which states that if you connect a line from a planet to the sun, that line will sweep out a certain unit of area for a given time at any point in the orbit.
3. The Harmonic Law, K = R cubed/T squared. Please excuse the non-mathematical notation, I'll get the format figured out eventually. This law states that for any object orbiting another object, the ratio of the radius of the orbit cubed to the period of the orbit squared is a constant value. To calculate the value of K for the sun we can use the earth's orbital parameters. Therefore K for the sun = 1 astronomical unit cubed/year squared. Mars is about 1.5 times further from the sun and takes 687 earth days to complete an orbit. The K value calculated from this data is 0.97 au cubed/ yr squared. The other planets return values very close to these numbers. Kepler did not know about Neptune, Uranus and Pluto, but we can calculate their K values and we find that they are also very close to 1.

There we are. We orbit the sun in an elliptical path and we happen to be nearest the sun on about 4 January each year. Our ellipse is very nearly a circle so we stay at nearly the same distance from the sun all year.

The Kepler Museum in Regensburg, Germany has a very informative and interesting display regarding Kepler's life and work.

This is not an official federal paid holiday, but I hope that you will celebrate anyway.